This invention relates to a method of magnet design and magnet configurations produced by the method. In particular, the invention relates to asymmetric superconducting magnets for magnetic resonance imaging (MR imaging) and methods for designing such magnets.
The generation of strong and pure magnetic fields is of great interest in many technical applications. In particular, it is very important for clinical magnetic resonance imaging (MRI). A major specification of the static field in MRI is that it has to be substantially homogeneous over a predetermined region, known in the art as the xe2x80x9cdiameter spherical imaging volumexe2x80x9d or xe2x80x9cdsv.xe2x80x9d Errors less than 20 parts per million peak-to-peak (or 10 parts per million rms) over a dsv having a diameter of 45-50 cm are often required. Conventional medical MRI systems are typically around 1.6-2.0 m in length with free bore diameters in the range of 0.8-1.0 m. Normally, the magnet is symmetric and the midpoint of the dsv is located at the geometric center of the magnet""s structure. The central uniformity of symmetrical fields is often analyzed by a zonal spherical harmonic expansion.
The basic components of a magnet system 10 useful for performing magnetic resonance investigations are shown in FIG. 14. The system of this figure is suitable for producing diagnostic images for human studies, similar systems being used for other applications.
System 10 includes magnet housing 12, superconducting magnet 13, shim coils 14, gradient coils 16, RF coils 18, and patient table 20. As is well known in the art, magnet 13 serves to produce a substantially uniform field (the B0 field) in the dsv. Discussions of MRI, including magnet systems for use in conducting MRI studies, can be found in, for example, Mansfield et al., NMR in Imaging and Biomedicine, Academic Press, Orlando, Fla., 1982. See also McDougall, U.S. Pat. No. 4,689,591; McDougall et al., U.S. Pat. No. 4,701,736; Dorri et al., U.S. Pat. No. 5,416,415; Dorri et al., U.S. Pat. No. 5,428,292; and Chari et al., International Publication No. WO 94/06034.
In modern medical imaging, there is a distinct and long-felt need for magnet systems which have a shorter overall length. The typical patient aperture of a conventional MRI machine is a cylindrical space having a diameter of about 0.6-0.8 meters, i.e., just large enough to accept the patient""s shoulders, and a length of about 2.0 meters or more. The patient""s head and upper torso are normally located near the center of the patient aperture, which means that they are typically about a meter from the end of the magnet system.
Not surprisingly, many patients suffer from claustrophobia when placed in such a space. Also, the distance of the patient""s head and torso from the end of the magnet system means that physicians cannot easily assist or personally monitor the patient during an MRI procedure, which can last as long as an hour or two.
In addition to its affects on the patient, the length of the magnet is a primary factor in determining the cost of an MRI machine, as well as the costs involved in the siting of such a machine. In order to be safely used, MRI machines often need to be shielded so that the magnetic fields surrounding the machine at the location of the operator are below FDA-specified exposure levels. By means of shielding, the operator can be safely sited much closer to the magnet than in an unshielded system. Longer magnets require more internal shielding and larger shielded rooms for such safe usage, thus leading to higher costs.
In recent years, there has been an increasing interest in the optimal design of clinical MRI magnets. See, for example, M. W. Garrett, xe2x80x9cAxially symmetric systems for generating and measuring magnetic fields. Part I,xe2x80x9d J. Appl. Phys. 22, 1091-1107 (1951); M. W. Garrett, xe2x80x9cThick cylindrical coil systems for strong magnetic fields with field or gradient homogeneities of the 6th to 20th order,xe2x80x9d J. Appl. Phys. 38, 2563-2586 (1967); H. Siebold, xe2x80x9cDesign optimization of main, gradient and RF field coils for MR imaging,xe2x80x9d IEEE Trans. Magn. 26, 841-846 (1990); F. J. Davies, R. T. Elliott, and D. G. Hawkesworth, xe2x80x9cA 2-Tesla active shield magnet for whole body imaging and spectroscopy,xe2x80x9d IEEE Trans. Magn. 27, 1677-1680 (1991); A. K. Kalafala, xe2x80x9cOptimized configurations for actively shielded magnetic resonance imaging magnets,xe2x80x9d IEEE Trans. Magn. 27, 1696-1699 (1991); and W. M. Schmidt, R. R. Huson, W. W. Mackay, and R. M. Rocha, xe2x80x9cA 4 Tesla/ 1 meter superferric MRI magnet,xe2x80x9d IEEE Trans. Magn. 27, 1681-1684 (1991).
In addition to the above work, Pissanetzky has proposed an approach to field design based on a hybridized methodology incorporating ideas from finite elements, analytical techniques, and other numerical methods. See S. Pissanetzky, xe2x80x9cStructured coil for NMR applications,xe2x80x9d IEEE Trans. Magn., 28, 1961-1968 (1992). Thompson has illustrated a method based on a variational approach with constraints introduced by Lagrange multipliers. The analytical aspects of the variational calculus were combined with numerical techniques to obtain optimal spatial coil distributions. See Michael R. Thompson, Robert W. Brown, and Vishnu C. Srivastava, xe2x80x9cAn inverse approach to design of MRI main magnetsxe2x80x9d, IEEE Trans. Magn., 30, 108-112, (1994); and Robert W. Brown, Hiroyukai Fujita, Shmaryu M. Shvartsman, Michael R. Thompson, Michael A. Morich, Labros S. Petropoulos, and Vishnu C. Srivastava, xe2x80x9cNew applications of inverse methods in the design of MRI coilsxe2x80x9d, Int. J. of Applied Electromagnetics and Mechanics, 9, 277-290, (1998). Crozier has introduced a stochastic optimization technique that was successfully used to design symmetric, compact MRI magnets. See S. Crozier and D. M. Doddrell, xe2x80x9cCompact MRI magnet design by stochastic optimization,xe2x80x9d J. Magn. Reson.127, 233-237 (1997); and U.S. Pat. No. 5,818,319.
In general, the design of superconducting MRI magnets requires the consideration of various parameters. These include: central magnetic field strength, peak field in the superconductors, spatial homogeneity within the dsv, geometrical constraints, weight, and cost. The challenge in designing a compact magnet is the retention of high homogeneity conditions in the dsv, as magnet homogeneity is strongly dependent on the overall length of the coil structure. A measure of this fact is the relaxation factor xcex3=d/R, (see FIG. 1a), where d is the distance from the end of the magnet to the beginning of the dsv on axis and R is the free bore radius. The smaller the value of xcex3, the more difficult it is to obtain a desired homogeneity level in the dsv.
In view of the foregoing, it is an object of the invention to provide high quality MR images and at the same time minimize the sense of claustrophobia experienced by patients and allow better access to patients by attending physicians.
More particularly, it is an object of the invention to provide MRI magnets which have a dsv diameter of at least 40 centimeters, a uniformity over the dsv of at least 20 ppm peak-to-peak, and a dsv location which is closer to one end of the magnet than the other, e.g., a dsv location where the midpoint M of the dsv is within 40 centimeters of an end of the magnet (see FIG. 1b).
It is also an object of the invention to provide methods of magnet design and magnet configurations produced by the methods which minimize the difficulties which have existed in the art in designing MRI magnets which have short lengths and/or offset dsv""s.
To achieve the foregoing and other objects, the invention in accordance with certain of its aspects provides a magnetic resonance system for producing MR images comprising an asymmetric superconducting magnet which produces a magnetic field which is substantially homogeneous over a dsv having a diameter greater than or equal to 40 centimeters, said magnet having a longitudinal axis (e.g., the xe2x80x9cz-axisxe2x80x9d) and comprising a plurality of current carrying coils which surround the axis, are distributed along the axis, and define a turn distribution function T(z) which varies with distance z along the axis and is equal to the sum of the number of turns in all coils at longitudinal position z, wherein:
(i) the longitudinal extent xe2x80x9cLxe2x80x9d of the plurality of coils (see FIG. 1b) defines first and second ends for the superconducting magnet, which, for example, can be spaced apart by a distance which is less than or equal to 1.4 meters and greater than or equal to 0.3 meters,
(ii) the variation of the longitudinal component of the magnetic field in the dsv is less than 20 parts per million peak-to-peak,
(iii) the dsv defines a midpoint xe2x80x9cMxe2x80x9d which is closer to the first end than to the second end,
(iv) the midpoint xe2x80x9cMxe2x80x9d of the dsv is spaced from the first end by a distance xe2x80x9cDxe2x80x9d which is less than or equal to 40 centimeters (preferably, less than or equal to 35 centimeters), and
(v) the turn distribution function T(z) has a maximum value which occurs at a longitudinal location that is closer to the first end than to the second end.
In accordance with the invention, it has been determined that to move a dsv towards one end of an MRI magnet (the xe2x80x9cfirst endxe2x80x9d) and still retain a high level of uniformity of the B0 field over the dsv, the turn distribution function must exhibit substantially larger values near said first end. Preferably, the maximum value of the turn distribution function T(z) occurs at the first end, although in some cases in can be displaced to some extent from that end.
The turn distribution function is calculated by summing the number of turns of all coils surrounding a particular longitudinal position regardless of the radial locations of the coils and regardless of the direction in which current flows through the coils (i.e., the turn distribution function is a count of the number of turns in all coils without regard to winding direction). The turn distribution function combines the effects of what would be referred to in classical MRI magnet design as primary and shielding coils, but does not include shim coils or gradient coils.
For the magnet designs of the invention, the terms xe2x80x9cprimaryxe2x80x9d and xe2x80x9cshieldingxe2x80x9d coils are, in general, not particularly meaningful since the coils of the magnet take on a variety of radial locations, axial locations, and winding directions in order to achieve the desired dsv characteristics, as well as, desired overall magnet geometry (e.g., the magnitude of xe2x80x9cLxe2x80x9d), desired stray field levels external to the magnet (e.g., stray field levels less than 5xc3x9710xe2x88x924 Tesla at all locations greater than 6 meters from the midpoint M of the dsv), and desired peak field strengths within the coils of the magnet (e.g., a peak magnetic field strength within the current carrying coils of less than 8.5 Tesla). Put another way, the coil designs of the invention exhibit a richness in distribution which makes the simplistic primary/shielding terminology of the prior art inappropriate.
In certain preferred embodiments, the MRI magnet will have a plurality of radially-stacked coils at the first end which are wound to carry currents in opposite directions. For example, at least one of the radially-stacked coils can be wound so as to carry current in a first direction and at least two others of those coils can be wound so as to carry current in a second direction opposite to the first direction. In certain embodiments, these two coils are located radially adjacent to one another. In other embodiments, the radially innermost and radially outermost of the radially-stacked coils are wound to carry current in the same direction.
According to another aspect, the invention provides a method of designing magnets for use in magnetic resonance imaging comprising the steps of:
(1) determining one or more desired current densities for a specified total magnet length L, a specified dsv diameter, a specified dsv position within the magnet, and a specified B0 field strength,
(2) determining an initial coil configuration from a plot of the one or more current densities determined in step (1), and
(3) optimizing the initial coil configuration to arrive at a final coil configuration for the magnet design.
More particularly, a method for designing a superconducting magnet having a longitudinal axis which lies along the z-axis of a three dimensional coordinate system is provided which comprises:
(a) selecting at least one cylindrical surface for current flow (e.g., 2 to 6 surfaces), said surface being located at a radius r1 from the longitudinal axis and having a preselected length L along said axis;
(b) selecting at least one constraint on the magnetic field produced by the superconducting magnet, said at least one constraint comprising the homogeneity of the magnetic field in the z-direction produced by the superconducting magnet over a predetermined region (the xe2x80x9cdsvxe2x80x9d);
(c) obtaining a vector Jr1(z) of current densities at the at least one cylindrical surface by solving the matrix equation:
AJr1(z)=Bxe2x80x83xe2x80x83(Equation I) 
where A is a matrix of unknown (non-linear) coefficients and B is a vector obtained by evaluating Biot-Savart integrals for each element of Jr1(Z) for the at least one constraint, said vector Jr1(z) of current densities being obtained by:
(i) transforming Equation I into a functional that can be solved using a preselected regularization technique, and
(ii) solving the functional using said regularization technique;
(d) selecting an initial set of coil geometries for the superconducting magnet using the vector Jr1(z) of current densities obtained in step (c); and
(e) determining final coil geometries for the superconducting magnet using a non-linear optimization technique applied to the initial set of coil geometries of step (d).
In the preferred embodiments of the invention, the selected at least one cylindrical surface for current flow has a first end and a second end, and step (b) in addition to requiring a specified homogeneity of the magnetic field in the z-direction over the dsv, also requires that:
(a) the dsv has a midpoint closer to the first end than to the second end; and/or
(b) the magnitude of the stray magnet fields produced by the superconducting magnet at at least one location external to the superconducting magnet (e.g., along the surface of an ellipse external to the magnet) is less than a specified level; and/or
(c) the peak magnetic field strength within the coils of the superconducting magnet is less than a specified level.
Preferably, all of constraints (a), (b), and (c) are simultaneously applied, along with the basic constraint that the magnetic field has a specified homogeneity in the z-direction over the dsv.
According to another aspect of the invention, magnet configurations suitable for use in MR imaging are produced by above method.